Initial reaction to yesterday's extensive Cabinet reshuffle suggests that the promotion of women did not resonate with the public as much as the Conservatives might have hoped.

Social media analysis commissioned by PRWeek shows the promotion of women was not as talked about among the general public as the departures of William Hague and Michael Gove from senior posts.

Exclusive research for PRWeek by Impact Social analysed 90,000 tweets mentioning #reshuffle yesterday. Gove’s demotion to Chief Whip represented 29 per cent of the conversation, with most mentions welcoming the departure of a "divisive" figure.

The second biggest share of the conversation was Hague’s surprise resignation, which attracted 16 per cent of the tweets, followed by the appointment of more women.

"Although the PM's tweet announcing Nicky Morgan as the new Education Secretary was the most shared, with over 1,000 retweets and favourites, only 12 per cent of mentions discussed the promotion of women and within these there was significant discussion of tokenism," says Impact Social director Will Brown.

A further five per cent of tweets to #reshuffle registered irritation that Iain Duncan-Smith kept his job at the Department for Work and Pensions, while 24 per cent of all mentions were negative in sentiment, with complaints that the Government had moved to the right.

Katie Perrior, director of iNHouse Communications, says the promotion of eight women would not necessarily go down well with 50 per cent of the electorate.

"There has been some slightly damaging PR around this with mixed messages," she says.

"The Tories have to make it more clear that these women have faced difficult selection processes to even become MPs and that they are capable of doing their jobs and running departments. It’s not window dressing but it could be seen as such. A better way of presenting it might not have been to refer to the fact that there were more women at all."

The shock demotion of Michael Gove from Education Secretary to Chief Whip was bound to overshadow the appointment of so many women to Cabinet posts, argues Ian Kirby, head of media at MHP Communications and former political editor at The News of the World.

He says: "They put a lot of work into it and all the women were promoted in time for the lunchtime news and paraded in front of the cameras, but the Gove demotion meant that the big headline the following day would be ‘Gove Out’.

"There are still twice as many boys from public schools in the Cabinet as there are women. It doesn’t solve the problem for them that the selection committees for MPs in constituencies still like people who are white, middle class and male.

"It’s not universal and there are constituencies that have adopted voluntary all-women shortlists or that have just chosen the right candidate but there are still too many that aren’t like that."

David Cameron and his ministers have repeatedly been accused of having a ‘women problem’ during the current Parliament – that is to say a deficit of them in senior Cabinet positions and policies that do not attract female voters.

"Cameron still has a ‘women problem’ although this reshuffle goes some way to wards building those bridges," says Perrior. "There is a real problem when women see the elite living a nice life while they are struggling to balance household budgets."